Nonminimal Derivative Couplings and Inflation in Generalized Theories of Gravity

TL;DR

This paper explores extended gravity theories with nonminimal derivative couplings, deriving field equations and cosmological models that naturally produce inflationary solutions and de Sitter attractors without relying on scalar potentials or cosmological constants.

Contribution

It introduces a class of extended gravity theories with specific derivative couplings and demonstrates their capability to generate inflationary solutions intrinsically.

Findings

Inflationary solutions arise without scalar potentials or cosmological constants.

De Sitter space is shown to be an attractor in these models.

Certain couplings are ruled out based on theoretical consistency.

Abstract

We study extended theories of gravity where nonminimal derivative couplings of the form $R^{kl}\phi_{, k}\phi_{, l}$ are present in the Lagrangian. We show how and why the other couplings of similar structure may be ruled out and then deduce the field equations and the related cosmological models. Finally, we get inflationary solutions which do follow neither from any effective scalar field potential nor from a cosmological constant introduced ``by hand'', and we show the de Sitter space--time to be an attractor solution.